Placing the largest similar copy of a convex polygon among polygonal obstacles

L. Paul Chew; Klara Kedem

doi:10.1145/73833.73853

Placing the largest similar copy of a convex polygon among polygonal obstacles

L. Paul Chew, Klara Kedem

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

15 Scopus citations

Abstract

Given a convex polygon I and an environment consisting of polygonal obstacles, we find the largest similar copy of 1 that does not intersect any of the obstacles. Allowing translation, rotation, and change-of-size, our method combines a new notion of Delaunay triangulation for points and edges with the well-known functions based on Davenport-Schinzel sequences producing an almost quadratic algorithm for the problem. Namely, if I is a convex k-gon and if Q has n corners and edges then we can find the placement of the largest similar copy of t in the environment Q in time O(k⁴ n λ₄ (kn) log n), where λ₄ is one of the almost-linear functions related to Davenport-Schinzel sequences. If the environment consists only of points then we can find the placement of the largest similar copy of P in time 0 (k²n λ₃ (kn) log n).

Original language	English
Title of host publication	Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989
Publisher	Association for Computing Machinery
Pages	167-174
Number of pages	8
ISBN (Electronic)	0897913183
DOIs	https://doi.org/10.1145/73833.73853
State	Published - 5 Jun 1989
Externally published	Yes
Event	5th Annual Symposium on Computational Geometry, SCG 1989 - Saarbruchen, Germany Duration: 5 Jun 1989 → 7 Jun 1989

Publication series

Name	Proceedings of the Annual Symposium on Computational Geometry
Volume	Part F130124

Conference

Conference	5th Annual Symposium on Computational Geometry, SCG 1989
Country/Territory	Germany
City	Saarbruchen
Period	5/06/89 → 7/06/89

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Mathematics

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10.1145/73833.73853

Cite this

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title = "Placing the largest similar copy of a convex polygon among polygonal obstacles",

abstract = "Given a convex polygon I and an environment consisting of polygonal obstacles, we find the largest similar copy of 1 that does not intersect any of the obstacles. Allowing translation, rotation, and change-of-size, our method combines a new notion of Delaunay triangulation for points and edges with the well-known functions based on Davenport-Schinzel sequences producing an almost quadratic algorithm for the problem. Namely, if I is a convex k-gon and if Q has n corners and edges then we can find the placement of the largest similar copy of t in the environment Q in time O(k4 n λ4 (kn) log n), where λ4 is one of the almost-linear functions related to Davenport-Schinzel sequences. If the environment consists only of points then we can find the placement of the largest similar copy of P in time 0 (k2n λ3 (kn) log n).",

author = "{Paul Chew}, L. and Klara Kedem",

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language = "English",

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Paul Chew, L & Kedem, K 1989, Placing the largest similar copy of a convex polygon among polygonal obstacles. in Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Proceedings of the Annual Symposium on Computational Geometry, vol. Part F130124, Association for Computing Machinery, pp. 167-174, 5th Annual Symposium on Computational Geometry, SCG 1989, Saarbruchen, Germany, 5/06/89. https://doi.org/10.1145/73833.73853

Placing the largest similar copy of a convex polygon among polygonal obstacles. / Paul Chew, L.; Kedem, Klara.
Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Association for Computing Machinery, 1989. p. 167-174 (Proceedings of the Annual Symposium on Computational Geometry; Vol. Part F130124).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Placing the largest similar copy of a convex polygon among polygonal obstacles

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